Campus Units

Mathematics, Electrical and Computer Engineering

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

5-15-2016

Journal or Book Title

Linear Algebra and its Applications

Volume

497

First Page

66

Last Page

87

DOI

10.1016/j.laa.2016.02.018

Abstract

The distance matrix of a graph G is the matrix containing the pairwise distances between vertices. The distance eigenvalues of G are the eigenvalues of its distance matrix and they form the distance spectrum of G. We determine the distance spectra of double odd graphs and Doob graphs, completing the determination of distance spectra of distance regular graphs having exactly one positive distance eigenvalue. We characterize strongly regular graphs having more positive than negative distance eigenvalues. We give examples of graphs with few distinct distance eigenvalues but lacking regularity properties. We also determine the determinant and inertia of the distance matrices of lollipop and barbell graphs.

Comments

This is a manuscript of an article published as Aalipour, Ghodratollah, Aida Abiad, Zhanar Berikkyzy, Jay Cummings, Jessica De Silva, Wei Gao, Kristin Heysse et al. "On the distance spectra of graphs." Linear Algebra and its Applications 497 (2016): 66-87. DOI: 10.1016/j.laa.2016.02.018. Posted with permission.

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

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